Some years ago the late Dr. J. E. Gray of the British Museum described from the sea, off Margate, what he considered to be a new species of Porpoise, characterised by the presence on the dorsal fin of a row of stony tubercles. As a matter of fact it was subsequently shown that the Common Porpoise has the same structures, so that there was no need for a Margate species, _Phocaena tuberculifera_. Moreover, in the Indian _Neomeris_, a close ally of the Porpoise, a more abundant calcified covering of scales exists along the whole back of the animal. These plates, {343} it has been discovered, are larger in the foetus, a fact which naturally points to their being an inheritance from the past, now undergoing retrogressive changes. Such a way of looking upon the facts is confirmed by the finding, many years ago, by the naturalist and physiologist Johannes Mueller, of bony plates in connexion with the remains of a Zeuglodont Cetacean. It looks, therefore, very much as if the Eocene ancestors of the modern Cetacea had a skin studded with bony plates, as have the armadillos. This being the case, the disappearance of hair is not surprising. The room would be taken up by the calcified plates, and when the latter disappeared, as they have in the vast majority of existing Whales, the naked skin alone would be left. Whales possess no externally-visible hind-limbs; rudiments of these appendages are present, which will be dealt with under the description of the principal features of the skeleton. But it has been discovered that in the Porpoise, external vestiges of hind-limbs do appear in the foetus, a fact which, be it observed, does away with the old view that the flukes of the Whale are the last term in the series of vanishing hind-limbs, of which the Seals, with their hind-limbs and tail bound up together, offer an intermediate step. The tail is fish-like in form, but the flukes are horizontal instead of vertical as in fishes and _Ichthyosaurus_. This arrangement is no doubt associated with the need for rapid return to the surface waters after a prolonged immersion in search of food. A downward stroke, such as is given by the powerful and large tail flukes, would naturally bring about this result rapidly. The tail, moreover, is under all circumstances the swimming organ. Its motion has been stated to be slightly rotatory, like that of a screw, and it is the case that the two flukes are often alternate in shape like the flanges of a screw; one being convex upwards, the other convex downwards.